So far it seems that the ranking is merely cosmetic and doesn't have any impact on your gameplay. It's just a general indicator of how many tournaments you've won.

By "fight tokens," I assume you mean Victory Coins. These are a form of currency you receive from winning fights in any city, not just Las Vegas. You also get them, as you noted, from the Tournaments. If you go the Fight page in any city, you will see the number of Victory Coins you have in the upper right area of that page. These can be used to purchase items in the Marketplace under the Fight Club category.